Reasoning about Shared-Qubit Concurrency in Quantum Computing

Abstract

In this paper, we develop a semantic model for the parallel execution of quantum circuits, providing a formal foundation for studying shared-qubit concurrency in quantum computing. As in classical shared-memory concurrency, parallel quantum circuits may interfere with one another through operations on shared qubits. However, quantum entanglement and the noncommutativity of quantum operations introduce additional challenges for reasoning about their correctness. To address these challenges, we generalise the classical Owicki-Gries method to quantum computing at the level of quantum circuits. Our approach enables compositional reasoning about parallel quantum circuits by separating the verification of individual components from the analysis of interference between them. We formulate proof rules for establishing the correctness of parallel quantum circuits and prove their soundness with respect to the proposed semantic model.